Sapwood is softer than heartwood, so it will be weaker in general. However a sapwood-to-sapwood glue joint should be just as strong as the sapwood itself. And since we are talking about cutting boards, I’d say go for it.

I trim away softwood from my projects, but it has more to do with aesthetics than strength.

-- Willie, Washington "If You Choose Not To Decide, You Still Have Made a Choice" - Rush

What you are saying might be true for some particular odd species, but there is absolutely no truth to the idea in general terms. There is more sap wood being held together with glue than heart wood except for fine furniture and nowadays a lot of craftsmen even ignore that.